Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes

Jean-Marc Bardet (1) , Yakoub Boularouk (2) , Khedidja Djaballah (2)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 USTHB - Université des Sciences et de la Technologie Houari Boumediene = University of Sciences and Technology Houari Boumediene [Alger]

We prove the consistency and asymptotic normality of the Laplacian Quasi-Maximum Likelihood Estimator (QMLE) for a general class of causal time series including ARMA, AR($\infty$), GARCH, ARCH($\infty$), ARMA-GARCH, APARCH, ARMA-APARCH,..., processes. We notably exhibit the advantages (moment order and robustness) of this estimator compared to the classical Gaussian QMLE. Numerical simulations confirms the accuracy of this estimator.

Mots clés: Laplacian Quasi-Maximum Likelihood Estimator; Strong consistency; Asymptotic normality; ARMA-ARCH processes

Domaines: Statistiques [math.ST]

Jean-Marc Bardet, Yakoub Boularouk, Khedidja Djaballah. Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes. Electronic Journal of Statistics , 2017, 11 (1), pp.452-479. ⟨10.1214/17-EJS1241⟩. ⟨hal-01249503v2⟩